A pair of lines drawn through the origin forms a right angled isosceles triangle with right angle at the origin with the line 2 x+3 y=6 . The area (in sq. units) of the triangle thus formed is

Step-by-step solution

Any line through the origin making an angle of 45^ with the given line 2 x+3 y=6 is of the form y=m x where aligned & ( 45^ )= m- ( -2 3 ) 1+m ( -2 3 ) = 1 & 3 m+2= (3-2 m) & m= 1 5 ,-5 aligned Hence the sides are x-5 y=0,5 x+y=0 and 2 x+3 y=6 If p be perpendicular from vertex A(0,0) to base, then p= 6 13 . Hence its area = 1 2 A L B C= 1 2 (p)(2 p)=p^2= 36 13 sq. units.